An electron is released from rest near an infinite non-conducting sheet of uniform surface charge density -σ. The magnitude of the rate of change of its de Broglie wavelength varies as 1/tⁿ. Find n.

Question

G1 Physics · Accepted Answer

The electric field of an infinite non-conducting sheet has constant magnitude, so the electron experiences constant acceleration a. Starting from rest: v = at. De Broglie wavelength is λ = h/(mv) = h/(mat). Thus, λ ∝ 1/t. Differentiate: |dλ/dt| ∝ 1/t². Therefore, n = 2.